A stick with a mass of m and a length of L is pivoted about one end so it can ro

Question

A stick with a mass of m and a length of L is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released.

Part A

As it swings through the vertical, calculatethe change in gravitational potential energy that has occurred. (use g as gravity)

Part B

As it swings through the vertical, calculate the angular speed of the stick.

Part C

As it swings through the vertical, calculate the linear speed of the end of the stick opposite the axis.

Part D

Find the ratio of the speed of a particle that has fallen a distance of

L, starting from rest, to the speed from part (C).

Explanation / Answer

A) Gravitational potential energy = m g h

B) The change in potential energy of the stick delta (Ep) = m g delta h = -m g L / 2

As the pivoting motion is frictionless, the energy is conserved. delta E = 0

delta (Ep) + delta (Ek) = 0

delta (Ek) = - delta (Ep) = m g L / 2

m v

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